The Valuation of Options with Restrictions on Preferences and Distributions

Abstract

This article develops a discrete-time, risk-neutral valuation relation (RNVR) for the pricing of contingent claims when preferences in the economy are characterized by decreasing absolute risk aversion and the marginal distribution of the underlying is an inverse coshnormal. The RNVR is applied to obtain closed-form expressions for calls and puts written on nondividendpaying stocks, futures contracts, foreign currencies, and dividend-paying stocks. Such pricing equations contain two parameters, the threshold and rescale parameters, not contained in the Black-Scholes valuation equation. Inverse-coshnormal option values make the approach look interesting.

Option Pricing with Random Risk Aversion

“…Functions h w and h v need not be the same and the transformed-normal family include several types of distributions that have been used extensively in option pricing e.g. the log-normal distribution used by Black and Scholes (1973), the normal distribution used by Brennan (1979), the displaced log-normal distribution used by Rubinstein (1983), the inverse cosh-normal and the S u distributions used by Camara (2001Camara ( , 2003, and the g-distribution used by Vitiello and Poon (2008) amongst others.…”

The Valuation of Currency Put Options

“…Certain utility functions of investor preferences omit changes in risk aversion altogether. In both [39] and [40] the utility function = (Wealth − Consumption), with increases in wealth being governed by an increase in the price of the option over time. Brennan [39] made an allowance for the probability of assessment of outcomes to vary.…”

“…Therefore, this study models investor preferences based on risk aversions. Both of these papers indicate that the utility function of the investor and that of the option have identical distributions (lognormal for [39], and hyperbolic cosine lognormal for [40]), since utility is only governed by price of the foreign currency. As this paper views utility as being determined by personal beliefs or demographic factors, price is not the only variable that explains utility of consumption.…”